# Contra MathOverflow

In principle, I really like the idea of MathOverflow, and I browse through the questions and answers there fairly regularly. Once in a while, I can’t help thinking I could add something to the discussion, and even when I’m incompetent, I think I can procastinate like the best of them by writing about topics which are unrelated to more pressing tasks at end… Then, why haven’t I contributed more than two minor comments to MO?

Well, I have to admit that I can’t help laughing my head off any time I see the list of badges at the end of a contributor’s profile page (well, metaphorically, at least…) The very idea of badges is already hilarious, but just reading those lists, I can’t help imagining “Necromancers” battling it off with “Mortarboards” about, maybe, what is the right definition of a weak infrabarelled semitanakian quasi-category (on the left, and of the third kind, of course).

And then I just can’t take it seriously. But for me, mathematics is a serious matter — like games are to a child.

### Kowalski

I am a professor of mathematics at ETH Zürich since 2008.

## 39 thoughts on “Contra MathOverflow”

1. ano says:

So instead of judging the site by the community and what its members do, your reactions to it are based on features of software that the people of Math Overflow didn’t have any part in developing? [:-)]

1. Yes… It’s just psychological — if I had thought of trying to start such a site (and I repeat the idea is excellent and I enjoy reading it), the first thing I would have done would have been to figure out a way to get rid of ridiculous things like that.

1. renaud says:

Hi, all the students who read your books and articles are on math.stackexchange.com and mathoverflow.net. Please understand that analytic number theory is not an easy subject, and mutual aid is really helpful. My opinion is that they are really serious mathematical websites.

2. Anonymous says:

Dear Emmanuel, there are many things about MO that irritate me greatly, not least of which is the ridiculous reputation system. It’s easy, however, to subvert that system simply by posting answers using randomly generated usernames. Your answers will then be appreciated by people who make the effort to read actual mathematics, and ignored by everyone else.

3. Mark Meckes says:

An alternative to using randomly generated usernames is to make all of your answers “community wiki”, which means you will not accrue “reputation” from them.

Personally I agree that the badges are ridiculous, though I find them easy enough to ignore. There is some sense to having the reputation system — users who have contributed a lot to the site earn the ability to do certain administrative tasks. If those tasks fell to only a handful of people, or were open to anyone who happened across the site, I don’t think it could function. But I don’t see any good reason that a user’s reputation score should be publicly viewable at all, let alone attached to user’s name everywhere it appears. Nevertheless, I again find reputation easy enough to ignore.

4. François G. Dorais says:

The only flaw with Anonymous’s strategy is that it takes 100 pts to leave comments. I would suggest keeping one stable user with the minimum 100 pts for commenting purposes.

There is also BCnrd’s strategy to only answer in comment form, thereby avoiding receiving any points for answers.

Finally, I would advise anyone who wants to use Anonymous’s strategy to refrain from voting. The system has features that detect suspicious voting patterns such as would be created by a person with multiple users voting for each other.

5. François G. Dorais says:

(Erratum: I meant 50 pts, not 100 pts.)

6. Anonymous says:

Dear François, unregistered members can’t vote anyway. Not that there is much of a point to voting, the correlation between interesting mathematics and votes being well known to be negative (mostly due to the effect of the popularity of soft questions, but not entirely).

The other reason for anonymity is to require the reader to actually read the mathematical content. I have seen a comment by Brian which was both wrong and had no details receive 5 upvotes before Brian came back and corrected it.

7. It would be possible, even with our currently limited access to the software, to add a user preference so that no user reputations, or badges, are shown to you. If people are interested, we should discuss this on meta.

I don’t think it would be feasible at this point to “opt-out” of the reputation system, so no one can see your reputation, but I’ll think about this more.

8. If I may be so bold as not to decry the orthodoxy… I think it is stretching a point to say that correlation between interesting mathematics and votes is negative; I speak as someone who has looked at his fair share of questions which got negative votes and deserved them.

My own feeling is that “value” or “interest”, inasmuch as they could possibly be meaningful as measures here, are more like Cne^{-n} for some constant C, with n being the number of votes.

9. A.J. says:

Coming up with ways of avoiding the reputation system strikes me as taking it a bit too seriously. Reputation is, I’d say, generally more correlated with participation than mathematical prowess.

10. This thread sparked a discussion on meta.mathoverflow.net. In particular, I posted my thoughts there. Basically, I defend badges and reputation, and also acknowledge that they can be silly.

I don’t think anybody believes that everything about a system must be completely serious for it to warrant being taken seriously. Saying that you can’t take MathOverflow seriously because the badges are silly strikes me a bit like saying you can’t take a person seriously if they’ve ever told you a funny joke.

11. “Saying that you can’t take MathOverflow seriously because the badges are silly strikes me a bit like saying you can’t take a person seriously if they’ve ever told you a funny joke.”

Au contraire, I often have trouble taking people “seriously” (unfortunately, the word has shades of meaning going in almost opposite directions in what JSE would call my idiolect; this “serious” is the positive one) unless they show they have a sense of humor and can enjoy jokes. But — and this is a personal opinion — I don’t find the badges funny at all…

12. Mark Meckes says:

Perhaps Anton’s point would be made more aptly by “Saying that you can’t take MathOverflow seriously because of the badges is a bit like saying you can’t take a person seriously if they’ve ever told you a bad joke.” Or maybe more aptly still by “… if they frequently tell bad jokes.”

13. MikeB says:

Kowalski, is your issue with badges and the reputation system, less of issue with the system itself and more with the possible disconnect between a given users knowledge and there level with respect to the reputation system? In the sense that, you are less likely to respect a user with hundreds of badges and thousands of points, simply because you view the fact that spending the time and effort needed to achieve such a level as silly? (I apologize for any errors in grammar, or spelling)

14. I find that I don’t notice the badges any more than i notice the advertisements on Facebook or Google. On the other hand, I rather like the reputation system. Despite being a grown man, I find it makes me more likely to answer questions.

15. I didn’t say anything about the reputation/point system…

The comparison with ads is interesting. I don’t mind (and barely see them) on Google, but I’m not contributing “anything” to Google by using their services (I know: I do at least contribute to their market share); and I don’t use Facebook as a principle (I don’t trust them at all). MathOverflow is therefore different (for me)…

16. I made some comments on the meta thread mistakenly believing that Dr. Kowalski was participating in the discussion, so I will attempt to summarize my position here as well.

I think of MO participation as an extremely efficient way to create a public good. When you give a good answer to a good question, not only have you probably helped someone get unstuck in their research, which saves them countless hours, but the resulting discussion probably teaches many of its viewers something new about the subject of the question. In addition, the software gives MO questions high PageRank, so they are easy to find on Google. Hence if a future student or researcher has a similar question, it becomes very easy for them to find it and be enlightened.

The result is a powerful ripple effect: many, many people are learning from even a single good answer. Given that the effect of good participation is so large compared to its cost (perhaps ten minutes of an expert’s time), I find it kind of silly to let any purely aesthetic choices about the design of the website get in the way.

To give a slightly better metaphor than the one I used in the meta thread, the situation is a little like the following: a charity has a donation box which multiplies any donations it receives by 100. You are about to donate your pocket change, but are stopped because you think the smiley faces on the donation box look kind of silly.

17. Well, I appreciate your enthusiasm, but honestly I don’t find your position convincing. For the record, I did follow the meta discussion, but since most of it concerned the reputation number system, which I haven’t much opinion about (except that I don’t really care), I didn’t feel any urge to contribute. (And as a matter of principle, where I give opinions, I do so non-anymously.)

To come back to your response: I have been a graduate student and a researcher spending a lot of time looking for an answer to a question that I was pretty sure existed somewhere. As it turns out, I can’t recall a single case where doing this did not bring enormous, unexpected, positive consequences. (Coincidentally, there’s an example in my previous post on this blog; and my career would certainly have been very different if I had stumbled too early on an elementary proof of the fact that

$a^n-1\text{ divides } b^n-1$

for all $n$ implies that $a$ divides $b$.)

So I can’t feel particularly concerned about students working hyperbolic “countless hours” on this type of work, especially since I’m happy to try to answer questions I receive by email, time permitting.

But as I said again, I like the MathOverflow site anyway; and as I’ve said, I have contributed two comments, so obviously I’m not entirely unconvinced about even participating. I’m inclined to think, following one Anonymous’s idea, that the next time I feel like I can add to a discussion, I’ll just use a clever nom de plume, or as we say in French, un pseudonyme transparent. I’m even very tempted to use more than one — I have a few excellent ones all ready from previous literary exercises — so that I can start indulging every once in a while in my intermittent ultra-Bourbakist tendancies…

18. That is a very good point. Certainly I try not to ask every question that pops into my head on MO (or at least, not anymore) because I have also found that I gain a great deal from working out the answer myself. Actually, I think the point has been brought up before that having a resource that makes it too easy to ask questions might rob students of the process of struggling through those questions themselves, but I haven’t thought about it in awhile. Hmm.

19. “having a resource that makes it too easy to ask questions might rob students of the process of struggling through those questions themselves”

I’m of the opinion that it’s not possible to rob somebody in this way. Acquiring mathematical understanding is hard no matter how much somebody holds your hand. I’ve never felt that somebody “ruined” some area of mathematics for me by explaining something about it. I suspect that nobody else has either.

There might be more to this objection, but I think the first gut-reaction version of it just doesn’t hold water. If somebody suggested, “students shouldn’t learn about exact sequences because they make it too easy to prove things,” I’m confident everybody would disagree. What important difference is there between knowing about exact sequences and having access to a large body of experts?

20. You are responding to someone else, but I’d like to say that your personal opinion has little to do with the truth in such matters when it comes to other people, whose mind might well work differently than yours. I know that when I need some result, I usually much prefer, at first, to try to think it through by myself, and I’ve been known to avoid even searching the literature for some time while trying to do that. And I seriously doubt that I’m the only one (this is based on conversations with some much better mathematicians than me)…

21. Indeed it is unclear why Emannuel’s concern about badges (and even more about the names for the badges rather than the badge system itself,) is related to participating in MO. Contributing answers to MO is an altruistic thing so it is not clear why people would spend time on it anyhow. Even if one is interested in outreach/altruistic activity there are several other possibilities (e.g. writing a blog).

There are various other concerns about the usefulness of MO and other Internet mathematical activities. The fact that communication is so much easier than before gives sometime the illusion that if we seek for an answer all we need is to ask around. Certainly, there are many cases where the answer is simply not known and there are also advantages to try to come up with the answer by yourself. (There are examples of famous mathematicians that did not read papers by others and tried always to do everything from scratch. But there are even more examples of famous mathematicians with the power to read/listen/grasp what others do.)

Overall MO is a very good thing. It gives people (especially those not located in central places) the opportunity to get information from and communicate with experts.

22. I tend to care about names and words, probably more than most mathematicians (judging e.g. from the first paragraphs of most papers I get to read…) I just can’t fathom the mind of anyone _creating_ the badge system — it’s just puerile beyond (my) belief. (And honestly, if it hadn’t been already in the software, would anyone ever have thought “Geez, this can’t possibly work! We can’t give anyone a necromancer badge!”)

[Unrelated to this last comment, and a bit off-topic, I’m sure that I’m not the only French person to be reminded of the song of Georges Brassens whenever reputation systems are mentioned:

Au village, sans prétention,
J’ai mauvaise réputation.
Que je me démène ou que je reste coi
Je passe pour un je-ne-sais-quoi!
Je ne fait pourtant de tort à personne
En suivant mon chemin de petit bonhomme.
Mais les braves gens n’aiment pas que
L’on suive une autre route qu’eux,
Non les braves gens n’aiment pas que
L’on suive une autre route qu’eux,
Tout le monde médit de moi,
Sauf les muets, ça va de soi.

(etc..)

23. “I’ve been known to avoid even searching the literature for some time while trying to do that.”

I think that sentence makes my point. I assume you wouldn’t argue that it’s a shame that the literature *exists*. Of course it is invaluable to think through something yourself. It’s hard to imagine anyone who would disagree, but that is not in question. What is in question is whether access to the literature, or experts, or Google actually prevents people from thinking deeply/individually/creatively about things. I have yet to see evidence that it does. As far as I can tell, whenever someones brain cycles are freed up by some technology or tool, they put those cycles to good use elsewhere.

24. >I assume you wouldn’t argue that…

Please let us not assume too much that we know what other people think — it’s tempting but it’s a bad idea to build dialogue. Everything I’ve said has been about my own opinions, or sometime mere instinctive reactions. The line from me that you quote and answer was itself written in a reply to Qiaochu Yuan, and you can follow the back-and-forth there to see that I never presumed to argue that anything I wrote was valid in greater generality than in my own mind…

> As far as I can tell, whenever someones brain cycles are freed up by some technology or tool, they put those cycles to good use elsewhere.

To some use, maybe, but why necessarily “good”? Alas, human history is full of very bad uses of technology.

25. >I never presumed to argue that
>anything I wrote was valid in greater
>generality than in my own mind…

OK, that was exaggerated, since I did say in the comment just before Gil Kalai’s that I had the impression that some other mathematicians had some similar opinions… But even that was qualified as being my own impression, so the basic point in my previous comment remains.

26. ano says:

After reading all these comments, I (not a regular user of MathOverflow, but somewhat familiar with it) still can’t figure out what exactly your objection is based on. As I understand it, you are so bothered by a bunch of unimportant names being “puerile” that it prevents you from the altruistic/fun/time-wasting/whatever activity that participation on MathOverflow would be… but it wouldn’t prevent you from participating anonymously? Is it that you are afraid that labels like “Necromancer” may get attached to your account (easy to avoid, BTW) and that unlike most people on MathOverflow who don’t pay any attention to these, someone may notice it in your profile and use it to form judgment about you?

27. >Is it that you are afraid that labels like “Necromancer” may get attached
> to your account (easy to avoid, BTW) and that unlike most people on MathOverflow
>who don’t pay any attention to these, someone may notice it in your
>profile and use it to form judgment about you?

No.

I have said a few times that my reaction is instinctive. As such, I am aware that whatever I say, it might be hard to understand. I don’t claim that it is logical, right, or correct. It is just my reaction. Anybody is free to dismiss it (but note that the overwhelming majority of research mathematicians, even fairly young ones, have no online presence whatsoever, however enthusiastic they are as mathematicians or teachers.)

As for participating anonymously, note that my preferred way would/will be pseudonymously, which is not the same thing at all. I will be very happy, under an assumed name, to try to acquire as many badges as possible. Unfortunately, my limited mathematical abilities make it unlikely that I could corner the market for these shiny tokens of excellence…

28. I have to say, as someone who participates on Math Overflow and who doesn’t seem to share Emmanuel’s misgivings, I find the number (and occasionally the tone) of responses here somewhat baffling. As I read it, he merely expressed a personal and instinctive view, only to find (metaphorically speaking) the Church of Latter Day Saints on his doorstep. Chacun a son gout.

29. Nice metaphor… (Nitpick on the French quote: one should write “Chacun son goût”…)

30. I must admit that I looked up what ‘necromancer’ means only well after I encountered the word in MO so for me the original meaning is “Answered a question more than 60 days later with at least 5 votes”. I suppose this resembles what most young people regard as the genuine meaning of the word “mouse” these days.

31. Anon says:

Lurking in Mathoverflow is also a precious experience. One witnesses firsthand just how nasty can certain people behave. One gets to see it without the misfortune of directly interacting with these people. They are also conveniently highlighted thanks to diamonds, reputation and badges.

32. This last comment is not relevant at all to this post — I hope there won’t be more like that.

33. Richard says:

You could do what I do whenever I encounter something that irritates me (rationally or otherwise) on a web site: attempt to elide it using Adblock.

mathoverflow.net##.user-page .item-multiplier